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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-7/4, b>=a > For fixed z and a=-7/4, b=21/4





http://functions.wolfram.com/07.23.03.affb.01









  


  










Input Form





Hypergeometric2F1[-(7/4), 21/4, 3/2, z] == (1/(9945 Pi^(3/2) Sqrt[z])) (2 ((2 (1617 - 35109 z + 129664 z^2 - 161792 z^3 + 65536 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^2 - (2 (1617 - 35109 z + 129664 z^2 - 161792 z^3 + 65536 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^2 - (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z]))) ((1617 - 5781 Sqrt[z] - 29328 z + 52864 z^(3/2) + 76800 z^2 - 112640 z^(5/2) - 49152 z^3 + 65536 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/(-1 - Sqrt[z] + z + z^(3/2))) ((-1617 - 5781 Sqrt[z] + 29328 z + 52864 z^(3/2) - 76800 z^2 - 112640 z^(5/2) + 49152 z^3 + 65536 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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<apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02